It is known that 5% of all men and .25% of all women are color-blind. A person is chosen randomly and it is determined that the person is color blind. What is the probability that this is a man? (It is assumed there is an equal number of men and women.)

I attempted part of it, not sure if I did it correctly.

5. It is known that 5% of all men and 0.25% of all women are color-blind. A person is chosen randomly and it is determined that the person is color blind. What is the probability that this is a man? (It is assumed that there is an equal number of men and women.) What do I know? M= men col W=Women C= colorblind c = color blind . P ( CIM ) = . 05 P (C / W ) :. 25 What do I want to find out? PI MIC ) What do we expect the answer to be? P( MIC ) > . 05 How do I go from what I know to what I want to find? conditional P (MIC ) = P(CIM ) P (C ) Is the answer consistent with what I expected